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On the Distribution of a Sum of Sarmanov Distributed Random Variables

Author

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  • Raluca Vernic

    (Ovidius University of Constanta
    Institute for Mathematical Statistics and Applied Mathematics)

Abstract

Built from given marginals with a flexible dependency structure, Sarmanov’s family of multivariate distributions became of interest in various fields. In this paper, we present some formulas for the density of the sum of several random variables joined by Sarmanov’s distribution, with accent on the particular case of exponentially distributed marginals. Such results are useful in solving, e.g., financial and actuarial problems.

Suggested Citation

  • Raluca Vernic, 2016. "On the Distribution of a Sum of Sarmanov Distributed Random Variables," Journal of Theoretical Probability, Springer, vol. 29(1), pages 118-142, March.
    • Handle: RePEc:spr:jotpro:v:29:y:2016:i:1:d:10.1007_s10959-014-0571-y
    DOI: 10.1007/s10959-014-0571-y
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    References listed on IDEAS

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    1. Peter J. Danaher & Michael S. Smith, 2011. "Modeling Multivariate Distributions Using Copulas: Applications in Marketing," Marketing Science, INFORMS, vol. 30(1), pages 4-21, 01-02.
    2. Dhaene, J. & Henrard, L. & Landsman, Z. & Vandendorpe, A. & Vanduffel, S., 2008. "Some results on the CTE-based capital allocation rule," Insurance: Mathematics and Economics, Elsevier, vol. 42(2), pages 855-863, April.
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    Cited by:

    1. Yiqing Chen & Jiajun Liu & Yang Yang, 2023. "Ruin under Light-Tailed or Moderately Heavy-Tailed Insurance Risks Interplayed with Financial Risks," Methodology and Computing in Applied Probability, Springer, vol. 25(1), pages 1-26, March.
    2. Rafał Wójcik & Charlie Wusuo Liu, 2022. "Bivariate Copula Trees for Gross Loss Aggregation with Positively Dependent Risks," Risks, MDPI, vol. 10(8), pages 1-24, July.

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